Abstract:

Modal transition systems are a well-established specification formalism for a high-level modelling of component-based software systems. We present a novel extension of the formalism called modal transition systems with durations where time durations are modelled as controllable or uncontrollable intervals. We further equip the model with two kinds of quantitative aspects: each action has its own running cost per time unit, and actions may require several hardware components of different costs. We ask the question, given a fixed budget for the hardware components, what is the implementation with the cheapest long-run average reward. We give an algorithm for computing such optimal implementations via a reduction to a new extension of mean payoff games with time durations and analyse the complexity of the algorithm.

Parametric Modal Transition Systems

Abstract:

Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently
known extensions are incapable of expressing some practically needed aspects in the refinement process like exclusive, conditional and persistent choices.
We introduce a new model called parametric modal transition systems (PMTS) together with a general modal refinement notion that overcome many of the limitations and we investigate the computational complexity of modal refinement checking.

Abstract:

Modal transition systems (MTS), a specification
formalism introduced more than 20 years
ago, has recently received a considerable attention in
several different areas.
Many of the fundamental questions
related to MTSs have already been answered. However,
the problem of the exact computational complexity of thorough refinement
checking between two finite MTSs remained unsolved.

We settle down this question by showing EXPTIME-completeness
of thorough refinement checking on finite MTSs.
The upper-bound result relies on a novel algorithm running
in single exponential time providing a direct goal-oriented
way to decide thorough
refinement. If the right-hand side MTS is moreover deterministic,
or has a fixed size, the running time of the algorithm becomes polynomial.
The lower-bound proof
is achieved by reduction from the acceptance problem of
alternating linear bounded automata and the problem remains EXPTIME-hard
even if the left-hand side MTS is fixed.